The present invention relates to thermodynamic heat engines, in particular to improved efficiency thermodynamic heat engines of at least three cycle steps.
Prior thermodynamic engines of the Stirling cycle exchange a fluid that can be heated (or cooled) and compressed (or expanded) and have at least two different volumes or segregated portions or regions of a common volume in which the fluid is contained and moved. Typically, the fluid is generally heated to a first temperature T1 by a temperature source, cooled to a lower temperature T2 by a temperature sink and mechanical work extracted as a result of the displacement and expansion and compression of the fluid as it is cyclically exposed to the temperature source and sink. Notably, most of the heat received from the source is transferred to the sink, with a small portion (about 30%) being inefficiently converted to mechanical energy in a typical, good heat engine.
An exemplary reference Stirling cycle engine 50 is shown in FIG. 1 as a power piston and displacer system, with piston motion controlled by cam surfaces on the flywheel, but alternative methods of piston motion control may be incorporated by the Stirling cycle engine. As shown in FIG. 1, a volume contains the fluid (e.g. air) within a vessel 52 having thermal insulation there around. Typically, a displacer comprises a form of a baffle which divides the volume within the vessel 52 into two regions or portions of complementary varying size, specifically, a xe2x80x9ccoldxe2x80x9d end 52 C cooled to temperature T2 as provided by a heat sink 54 to the ambient temperature, and a xe2x80x9cwarmxe2x80x9d (or heated) end 52W heated by source 56 to temperature T1. The displacer is fitted within the vessel sufficiently completely so that fluid moves between the warm and cold regions substantially entirely via a regenerator 58 which is disposed in and moved with the displacer 60 within the volume 52 by the displacer 60 and rod 62. For simplicity, the piston and displacer rods in the exemplary embodiment of FIG. 1 are coaxial. That is, the displacer rod goes through the piston rod and the displacer rod goes over the flywheel axle (71 in FIG. 1.), which can be stationary and have a bearing interfacing with the flywheel 70. In this case, the axle or its assembly may be penetrated by the displacer rod. Alternate flywheel arrangements are possible in which the cam tracks do not cross and can be placed on opposite sides of the flywheel.
Mechanical energy output is provided by xe2x80x98powerxe2x80x99 piston 64 which in this embodiment, also incorporates a heat conductive material and the heat sink 54 attached thereto. The mechanical energy from the power piston is transferred to a flywheel 70 via connecting rod 74 and cam track 68, connected to or part of (together with the displacer cam track 72) the flywheel 70.
Stirling Cycle engines include constant volume processes (e.g. 84A and 88A) and constant temperature processes (e.g. 82B and 86B) cycles, as illustrated by the graphs 80A and 80B of FIGS. 2A and 2B, respectively. Also typically, as in other embodiments of the Stirling ling Cycle engine, the cyclical power piston and displacer motions of the embodiment of FIG. 1 are generally identical in sinusoidal motion, but offset by 90xc2x0. The typical piston and displacer positions-versus-time over the cycle reference points A-D (also in graphs 80A and 80B) are illustrated by respective segments 92P, 94P, 96P, 98P and 92D, 94D, 96D, 98D in the graph 90 of FIG. 2C.
The novel thermodynamic heat engines according to the present invention provide efficiencies higher than Carnot efficiency. In the present inventions, generally referred to as xe2x80x9cSuperclassical Cyclexe2x80x9d engines, constant volume cooling with displacement and regeneration, and aspects of the xe2x80x9cProell Effectxe2x80x9d (relative to cooling) are utilized. Moreover, the gas temperature on the cold side of a fluid displacer is below the lowest regenerator temperature due to xe2x80x9cself-refrigeration.xe2x80x9d
The xe2x80x9cProell Effectxe2x80x9d (as described in The Thermodynamic Theory and Engineering Design of Supercarnot Heat Engines, by Wayne Proell, Cloud Hill Press, Las Vegas, N.Mex., 1984) incorporated by reference, refers to thermodynamic heat engine cycles and includes previous behavior of all gases in constant volume conditions with regeneration. The Proell Effect, by itself, conforms to the most rigorous definition of the Second Law of Thermodynamics which calls for zero or greater than zero entropy increases in isolated energy systems. However, the Proell Effect is unrecognized, unpredicted and not fully explored for traditional analyses of constant volume processes, such as in the Stirling cycle engines. The Proell Effect is not seem in the Stirling cycle because of the summetry created by two constant volume processes of opposite direction of fluid flow which cancels the Proell Effect.
Conventional thermodynamics identifies only one behavior of gases in a constant volume process, that is a change in internal energy directly proportional to its temperature, which equates to the heat added or removed, as its heat capacity at constant volume, CV, times the temperature change experienced,
Q=CV(xcex94T)xe2x80x83xe2x80x83(1)
In addition to a description of gas behavior at constant volume as described by Equation 1, above, the constant volume environment and its energy flows become more complex when the constant volume is not at a uniform temperature and is divided by a displacer and the subdivided volumes are connected via a regenerator as illustrated by the engine 50 of FIG. 1.
Further understanding may be provided by the Proell Effect, wherein the fluid is exemplified by a gas. In a constant volume process with regeneration, the change in volume of a gas displaced through a regenerator as a result of its change in temperature going from the hot side (T1) of a constant volume to the cold side (T2) of a constant volume, or vice-versa, the gas being separated in the constant volume and displaced from said hot and cold sides through a regenerator by a displacer, must be compensated by an equal and opposite volume change in the remainder of the gas not in the regenerator, in the hot and cold sides of said constant volume. The corresponding pressure-volume work energies involved with all localized volume changes within the constant volume transfer thermal energy between said regenerator and the gas of the hot and cold sides of the constant volume. This results in a temperature change experienced by the gas under adiabatic conditions in the hot and cold sides of the constant volume which will be greater than the temperature difference of said regenerator, up to a limit proportional to said gas"" heat capacity ratio, gamma. The pressure-volume work transfers heat inside the regenerator by heat capacity at constant pressure CP and transfers heat by heat capacity at constant volume, CV, in said hot and cold sides of the constant volume.
The Proell effect may occur for fluid (gas) flow in either direction through the regenerator. When the gas going through the regenerator is heated, it expands, causing a compensatory compression in the remainder of the gas in the constant volume chamber. When the gas going through the regenerator is cooled, it compresses, causing a compensatory expansion in the remainder of the gas in the constant volume chamber. By normal gas behavior under adiabatic conditions, expansion is accompanied by a drop in temperature and compression is accompanied by a rise in temperature. These temperature changes are in addition to the temperature changes caused by intimate thermal contact with the regenerator while passing through the regenerator.
In the present invention, the final gas temperature on the cold side of the displacer in constant volume cooling is below the lowest regenerator temperature. The magnitude of how far below the conventional constant volume cooling temperature the gas goes depends upon the temperature difference of the regenerator and the degree of displacement. Such cooling beyond the conventionally predicted temperature is referred to as xe2x80x9cself-refrigeration.xe2x80x9d
When displacement from the hot side to the cold side is complete, half of the maximum self-refrigeration is created in the cold side. This is because compensatory cooling occurs in both the hot and cold side portions of the constant volume during the entire constant volume displacement. Summed throughout the entire stroke, the hot and cold sides contribute the same total heat flow and pressure-volume work. As an increment of gas passing through the regenerator cools, by the Ideal Gas Law, its volume decreases in direct proportion to the temperature decrease,
dVincrement=(nR/Pincrement)dTregenerator,xe2x80x83xe2x80x83(2)
where n is the number of moles of gas, R is the gas constant, and pressure, P, is variable and incremental because the overall constant volume process will see a pressure decrease as the entire mass of gas is cooled from high to low temperature in a fixed total volume. When the incremental volume of gas going through the regenerator is insignificant relative to the total volume, P is essentially constant for that incremental passage. By this same equation (2), it is seen that as P reduces over the entire constant volume process, incremental V must increase. The pressure-volume work done on the cooling gas is incrementally constant during the entire constant volume stroke. This is supported in conventional thermodynamics; the difference between CP and CV is a constant, also called the gas constant, R.
The work contributions made by the hot and cold volumes outside the regenerator are linearly proportioned according to the hot and cold gas volumes which shift throughout the stroke. At the beginning of the constant volume stroke, all of the compensating expansion is provided by the hot side. Half way through the stroke, half of the expansion work comes from the hot side and half from the cold side. At the end of the stroke, all of the work comes from the cold side. Since the incremental compression work is constant throughout the stroke, the cold side self-refrigeration energy is merely half of the total pressure-volume work absorbed by the regenerator. The hot side portion of the gas must pass through the regenerator, giving its thermal condition to the regenerator. That gas leaves the regenerator at the lowest temperature of the regenerator and the self-refrigeration which it obtained on the hot side is no longer present as the gas enters the cold side. That self-refrigeration is stored in the hot side of the regenerator as a slight cooling of the hot entrance of the regenerator, to be fully reversed in the engine""s heating stroke.
When the displacement from the hot side to the cold side is partial, and starts with some gas already on the cold side, more than half of the self-refrigeration is on the cold side. This larger self-refrigeration can approach gamma times the conventional constant volume cooling value proportional to CV.
The heat absorbed by the regenerator is,
Q=CP(xcex94Tregen),xe2x80x83xe2x80x83(3)
as a mass of gas going through the regenerator experiences nearly constant pressure and must absorb the work of compression from its volume decrease. The compression work absorbed is passed on to the regenerator as heat.
Since the gas being cooled in the regenerator can only provide heat to the regenerator at CV, the extra energy of CP absorbed in the regenerator must come from the remainder of the gas, as mentioned above. This absorption of heat by the regenerator is also termed heat recovery or heat rejection (to the regenerator).
The compression work done inside the regenerator is the difference between CP and CV:                     W        =                              (                          Δ              ⁢                              xe2x80x83                            ⁢                              T                regen                                      )                    ⁢                      xe2x80x83                    ⁢                      C            v                    ⁢                      xe2x80x83                    ⁢                      (                          γ              -              1                        )                                              (        4        )                                          xe2x80x83                ⁢                  =                      P            ⁢                          xe2x80x83                        ⁢                                          (                                  ⅆ                  V                                )                            .                                                          (4A)            
The work was provided from the bulk of the gas outside of the regenerator under adiabatic conditions, so the work comes from the internal energy of the gas in the hot and cold zones,
W=CV(xcex94Tsr).xe2x80x83xe2x80x83(5)
The self refrigeration, xcex94Tsr, is summarized as follows,
xcex94Tsr=KP(xcex94Tregen)(xcex3xe2x88x921).xe2x80x83xe2x80x83(6)
For full displacement (proportionality fraction KP=0.5),
xcex94Tsr=0.5(xcex94Tregen)(xcex3xe2x88x921).xe2x80x83xe2x80x83(7)
For partial displacement, more complicated conditions apply, as reflected by the proportionality fraction. Since only part of the gas confined to constant volume is passed through the regenerator, not as much energy is transferred. Likewise, the amount of self-refrigeration energy removed from the cold side depends upon the proportion of the total gas which is always on the cold side and half of the gas which comes from the hot side, The self refrigeration temperature change becomes,
xcex94Tsr=(min. cold side mass fraction+0.5 hot side mass fraction)xc3x97(mass fraction transferred)(xcex94Tregen)(xcex3xe2x88x921).xe2x80x83xe2x80x83(8)
If the lowest temperature of the regenerator is room temperature, a constant volume cooling stroke with regeneration will result in the confined gas at a temperature below room temperature. Since this is accomplished by only the displacement of the gas from the hot side to the cold side, this uncommon form of refrigeration takes place at a very low cost to an engine cycle which incorporates it. Under reversible conditions, this refrigeration takes place with no work input, only a perturbation which approaches zero work. Under common, irreversible conditions, the friction and viscous drag of the displacer is very small. This uncommon cooling is applied in the present invention to create an xe2x80x98internalxe2x80x99 heat sink to which all heat flows and is then partially or completely sent to the regenerator over the range of temperatures in the regenerator. When partial displacement is used, the self-refrigeration is greater than what is needed to produce an internal heat sink to capture all compression energy and all friction and all thermal losses. Heat can flow to the internal heat sink from outside the engine, becoming part or all of the heat input to the engine, and a unity efficient engine becomes possible.
This novel engine efficiency is consistent with the Kinetic Theory of Heat, wherein the collisions of moving particles composing matter transfer kinetic energy, which is thermal energy which is never lost; thermal energy is perpetual. When work is created from this thermal energy, all energy leaving the thermal mass can become work. Conventional thermodynamics allows for processes to have complete conversion of heat into work, such as in the isothermal expansion of an ideal gas under reversible conditions; likewise, isentropic expansion is a unity efficient process, producing work from only the internal energy of the working gas. Such work may degrade back to thermal energy. Since work has no temperature, it may be dissipated back to heat at whatever the temperature of the receiving mass is. If this is the same mass which produced the work from thermal energy, the energy flow as heat has occurred with no net entropy increase. Conventional thermodynamics does not preclude this except by the general understanding of the Second Law of Thermodynamics.
Conventional thermodynamics can accommodate the present inventions with the following refinements to the Second Law of Thermodynamics: Work and heat may interchange perpetually, when first, since work has no entropy and may be dissipated as heat at any temperature, an energy system may have more than one equilibrium state, and second, when an engine creates an internal heat sink which is lower in temperature than the surrounding environment, and thus no heat will escape the engine.
Thus according to the apparatus and methods according to the present invention, the traditional Second Law requirement of energy losses in a heat engine is circumvented, and uses the Second Law""s fundamental principle, e.g. that heat flows from higher temperature to lower temperature, to advantage.
The more observable distinctions of the method and apparatus of the present invention can be seen in the corresponding individual and relative motions of the piston and the displacer. By contrast with a typical (e.g. Stirling) cycle which have piston (and other mechanism) motions which are a pure sinusoid having a period equal to the cyclical rotation of the engine, the present invention has a more complex piston and/or displacer excursions that move in motions, or motion harmonics, more complex than a pure sinusoid motion. This is most clearly seen in portions of the cycle according to the various embodiments of the present invention discussed below, which include a stationary period. Furthermore, the piston and displacer motions are different motions, not just similar but phase-shifted motions as frequently found in prior art engines.